The simultaneous heat exchanger network (HEN) synthesis optimization problem is generally formulated as a mixed integer nonlinear program (MINLP) by using the concept of HEN superstructures. Although non-linear program (NLP) formulations have also been proposed, they suffer from some limitations. In this work, a new formulation of the simultaneous approach for HEN synthesis is proposed by representing the HEN superstructure as a process graph. This representation allows any HEN network to be evolved by circulating appropriate enthalpy flows around a set of independent loops of the process graph. By exploiting this feature, a robust and efficient NLP problem is formulated. Compared to MINLP formulations a significant reduction in terms of the size of the problem is achieved. The proposed formulation can handle fixed charges of exchangers and also design constraints such as restricted, required and forbidden matches, variable target temperatures etc. The robustness and efficiency of our formulation is demonstrated through several examples for different initial solutions including those obtained using Pinch Technology for both superstructures proposed in the literature.